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5. If 8 acres produce 176 bushels of wheat, what will 34 acres produce?

Ans. 748 bushels.

6. If 9lb. of sugar cost 6s. what will 25lb cost? Ans. 16s. 8d.

When there is a remainder after dividing the product of the second and third terms by the first, reduce it to the next lower denomination, and divide as before.

7. A borrowed of B $250 for 7 months; afterwards B borrow ed of A $300; how long must he keep it to balance the former favor?

Ans. 5ms 25ds.

8. If 100 men can do a piece of work in 12 days, how many men can do the same in 3 days? Ans. 400 men.

9. A goldsmith sold a tankard weighing 39oz 15pwt for £10 12s; what was it per ounce ? az. pwt. £

39 15 10 12:: 1 Ans. 5s. 4d. 11. If the interest of $100 for one year be $6, what will be the interest of $336 för the same tinte? $ $ $

100:6::336 Ans. $20.16. 11. If $100 gain $6 in one year, in what time will a sum of money double at that rate, simple interest?

Syr. $

6:1:100 Ans. 16 yrs. 12. If $100 gain 86 in 12 months, in how many months will a sum of money double at that rate, simple interest?

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22. Bought 4 bales of cloth, each containing 6 pieces, and each piece containing 27 yards, at £16 4s per piece; what is the value of the whole and the price per yard?

Ans. £388 16s and 128 per yd. 23. If a hogshead, of rum cost $75.60, how much water must be added to it to reduce the price to 1 dollar per gallon?

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34. A cistern containing 230 gallons, has two pipes; by one it receives 50 gallons per hour, and by the other discharges 35 gals. hour; in what time will it Ans. 15h. 20m.

per Ans. 12 gal. be filled? 24. If a board be 9 inches wide, how much in length will make a square foot ? Ans. 16in.

9:144 :: 1

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35. If 40 rods in length and 4 in breadth make one acre, how many rods in breadth, that is 16 rods long, will make one acre ?

Ans. 10 rods.

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h

Ans. 123 miles. m deg m m 24 x 60: 360 × 50 :: 1

37. If the earth perform its diurnal revolution in 24 hours, in what time does a place on its surface move through one degree? 360°: 24:: 1° Ans. 4 minutes.

38. There is a cistern which has a pipe that will empty it in 6 hours; how many such pipes will be required to empty it in 20 minutes? Ans. 18 pipes.

39. What is the value of $642 against an estate which can pay only 69 cents on the dollar?

Ans. $442,98.

40. How many men must be employed to finish in 9 days, what 15 would do in 30 days? Ans. 50 men.

RULE OF THREE IN VULGAR FRACTIONS. Prepare the fractions by reduction, if necessary, and state the question by the general rule; invert the first term, and then multiply all the numerators together for a new numerator, and all, the denominators together for a new denominator; the new numerator, written over the new denominator, will be the answer required.

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* In assessing taxes, it is generally best, first to find what each dollar pays, and the product of each man's inventory, multiplied by this sum, will be the amount of his tax. In this case, the sum on the dollar, which is to be employed as a multiplier, must be expressed as a proper decimal of a dollar, and the product must be pointed according to the rule for the multiplication of decimals; thus 2 cents must be written .02, 3 cents, 03, 4 cents, .04, &c. It is sometimes the practice to make a table by multiplying the value on the dollar by 1, 2, 3, 4, &c. as follows:

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2. A certain school, consisting 4. The inventory of a certain of 60 scholars, is supported on school district is $4325, and the the polls of the scholars, and the sum to be raised on this inventoquarterly expense of the whole ry for the support of schools, is school is $75; what is that on $86.50; what is that on the dolthe scholar, and what does A paylar, and what is C's tax, whose per quarter, who has 3 scholars? | property inventories at $76.44 ? Ans. $1.25 on the scholar, and A pays $3.75 per quarter. 3. If a town, the inventory of which is $24600, pay $287, what will A's tax be, the inventory of whose estate is $525.75? dol. inv. Tax. dol.iny. 24600.00 287 :: 525.75: $6.133

Ans.

$4325: 86.50 :: 1 .02cts. Ans. and 76.44 X.02-$1.528 C's tax.

5. If a town, the inventory of which is $16436, pay a tax of 8493.08, what is that on the dol

lar ?

$16436 $493.08: 1: .03cts. Ans.

QUESTIONS.

1. How is the Single Rule of Three

known?

2. By what other names is it sometimes called?

3. Which of the given numbers is to be written down for the second term?

4. How is it to be determined which of the others is to possess the third place?

5. How do you proceed, after stating the question, to find the answer?

6. If the first and third terms be of different denominations, what is to be done?

7. What is to be done, if the second

:

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This table is constructed on the supposition that the tax amounts to three cents on the dollar, as in example 3d. USE.-What is B's tax, whose rateable property is $276? By the table it appears that $200 pay $6, that $70 pay $2.10, and that $6 pay 18 cents. Thus $200 is $6 00 70 2.10

Proceed in the same way to find each individual's tax, then add all the taxes together, and if their amount agree with the whole sum proposed to be raised, the work is right. It is $8.28 B's tax. sometimes best to assess the tax a trifle larger than the amount to be raised, to compensate for the loss of the fractions.

6

0.18

276

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2. DOUBLE RULE OF THREE.

The DOUBLE RULE OF THREE, sometimes called Compound Proportion, teaches to resolve such questions as require two or more statements in the Single Rule of Three.

In the Double Rule of Three, there are usually five numbers given to find a sixth, but there may be more, as seven or nine:

Rule.

1. Make the number, which is of the same kind as the required answer, the second term.

2. Take any two of the remaining numbers that are of the same kind, and place one for a first term, the other for a third term, according to the directions given in the Single Rule of Three; then take any other two of the same kind, and place them in the same way, and so on, till all are used.

3. Multiply the product of the third terms by the second term, and divide the result by the product of the first terms, and the quotient will be the answer required..

Examples.

1. A wall which is to be built to the height of 27 feet, was raised to the height of 9 feet by 12 men in 6 days; how many men must be employed to finish the wall in 4 days ?

27-9-18

9: 12: 18

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:

6

By taking 9 from 27, we find the wall is to be raised 18 feet higher, and it is required to know how many men will finish it in 4 days; consequently 12 must be made the second term. Now if we take two numbers of the same kind, viz. 9 and 18, it is plain that the 18 will require more men than the 9, supposing the time to be the same; then 9 must stand in the first place, 36) 1296 (36 Ans. and 18 in the third. Again; if we take the

108

12

108

216

216

other two of the same kind, viz. the 6 and 4, and suppose the work the same, it is evident that if the same work is required to be done in less time, the number of men must be increased; i. e. if the work done by 12 men in 6 days is to be done in 4 days more than 12 men must be employed; hence 6. must stand in the third place, and 4 in the first.

2. If a man travel 112 leagues in 29 days, when the days are 7 hours long, how far will he travel in 17 days, when they are 10 hours long?

29 112 17

The days, their length being considered equal, would 7: :: 10 require the answer to be less than 112. because in this case he could not travel so far in 17 as in 29 days; and the hours, without regarding the days, would require the answer to be greater than 112, for he could certainly travel further in 10 than in 7 hours, and these two compounded as in the statement, give the distance required.

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